Table of contents
1. Introduction
In computer science, a sorting algorithm is an algorithm that puts elements in a specific order. Sorting algorithms can be divided into internal sorting and external sorting. Internal sorting means that all data can be sorted in memory, while external sorting means that the amount of data is too large to be stored in memory. External memory is needed for sorting.
Simple selection sorting is an internal sorting algorithm. Its basic idea is: each time select the smallest (or largest) element from the data elements to be sorted and store it at the beginning of the sequence until all the data to be sorted The elements are lined up.
2. Algorithm ideas
Simple selection sorting is a sorting algorithm based on comparison. Its basic idea is to select the smallest (or largest) element from the data elements to be sorted each time, store it in the starting position of the sequence, and then select the smallest (or largest) element from the remaining unsorted elements. Continue to find the smallest (or largest) element among the elements and put it at the end of the sorted sequence. And so on until all elements are sorted.
The specific implementation steps of simple selection sort are as follows:
1. Traverse the sequence to be sorted and find the position of the smallest element.
2. Exchange the smallest element with the first element of the sequence.
3. In the remaining unsorted sequence, find the position of the smallest element.
4. Exchange the smallest element with the second element of the sequence.
5. Repeat the above steps until all elements are sorted.
The time complexity of simple selection sort is O(n^2), where n is the length of the sequence to be sorted. Although its time complexity is high, it still has certain application value in some small-scale data sorting because of its simple implementation and easy-to-understand code.
3. C++ implementation
1. Code implementation
The following is the C++ implementation code of simple selection sort:
void selectionSort(int arr[], int n) {
int i, j, minIndex, temp;
for (i = 0; i < n - 1; i++) {
minIndex = i;
for (j = i + 1; j < n; j++)
if (arr[j] < arr[minIndex])
minIndex = j;
temp = arr[minIndex];
arr[minIndex] = arr[i];
arr[i] = temp;
}
}2. Time complexity analysis
The time complexity of simple selection sort is O(n^2), where n is the length of the sequence to be sorted. The specific analysis is as follows:
- In the best case, the sequence to be sorted is already in order, and only needs to be compared n - 1 times, and the time complexity is O(n); - In the worst case, the
sequence to be sorted is in reverse order, and (n-1) needs to be compared +(n-2)+...+2+1 = n(n-1)/2 times, the time complexity is O(n^2); - on average, the time complexity is O(n^
2 ).
4. Optimization plan
Although the time complexity of simple selection sorting is high, it has an advantage that it requires fewer exchanges. Therefore, if the elements in the sequence to be sorted are relatively large, and the exchange is time-consuming, you can consider using simple selection sort.
In addition, if there are a large number of repeated elements in the sequence to be sorted, you can consider using a sorting algorithm with linear time complexity such as counting sort or bucket sort.
V. Summary
Simple Selection Sort is a simple but inefficient sorting algorithm with a time complexity of O(n^2). In practical applications, different sorting algorithms can be selected according to specific situations to achieve better sorting results.